Let the \(T\) -sample time-domain observation \(\mathbf {x} \in \mathbb {R}^T\)  be a mixture of a target speech \(\mathbf {s}\)  and noise \(\mathbf {n}\) , such that, \(\mathbf {x} = \mathbf {s} + \mathbf {n}\) . The goal of standard SE is to recover \(\mathbf {s}\)  from \(\mathbf {x}\) . A popular strategy in supervised SE is the time-domain mask-based method [1]}, [2]}, [3]}. As an implementation example, [3]} estimates masks for separating speech and noise by a mask prediction network and applies it to the representation of \(\mathbf {x}\)  encoded by an encoder. The estimated signals \(\mathbf {y} \in \mathbb {R}^{T \times 2}\)  are then re-synthesized using a decoder. Here, \(\mathbf {y}_{:, 1}\)  and \(\mathbf {y}_{:, 2}\)  are the estimates of speech and noise, respectively. Then, a mixture consistency projection layer [5]} is applied to ensure the sum of \(\mathbf {y}_{:, 1}\)  and \(\mathbf {y}_{:, 2}\)  equals \(\mathbf {x}\) :
\(\mathbf {y}_{:, 1} \leftarrow \mathbf {y}_{:, 1} + \zeta \mathbf {e}, \quad \mathbf {y}_{:, 2} \leftarrow \mathbf {y}_{:, 2} + (1 - \zeta ) \mathbf {e},\) 
